Hybrid halide perovskites such as methylammonium lead iodide (CH 3 NH 3 PbI 3 ) exhibit unusually low free-carrier concentrations despite being processed at low-temperatures from solution. We demonstrate, through quantum mechanical calculations, that an origin of this phenomenon is a prevalence of ionic over electronic disorder in stoichiometric materials. Schottky defect formation provides a mechanism to selfregulate the concentration of charge carriers through ionic compensation of charged point defects. The equilibrium charged vacancy concentration is predicted to exceed 0.4 % at room temperature. This behavior, which goes against established defect conventions for inorganic semiconductors, has implications for photovoltaic performance.

Reducing the thickness of a material to its two-dimensional (2D) limit can have dramatic consequences for its collective electronic states, including magnetism, superconductivity, and charge and spin ordering. An extreme case is TiTe2, where a charge density wave (CDW) emerges in the single-layer, which is absent for the bulk compound, and whose origin is still poorly understood. Here, we investigate the electronic band structure evolution across this CDW transition using temperature-dependent angle-resolved photoemission spectroscopy. Our study reveals an orbital-selective band hybridisation between the backfolded conduction and valence bands occurring at the CDW phase transition, which in turn leads to a significant electronic energy gain, underpinning the CDW transition. For the bulk compound, we show how this energy gain is almost completely suppressed due to the three-dimensionality of the electronic band structure, including via a kz-dependent band inversion which switches the orbital character of the valence states. Our study thus sheds new light on how control of the electronic dimensionality can be used to trigger the emergence of new collective states in 2D materials.